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2.3 GRAPHS THAT ENLIGHTEN AND GRAPHS THAT DECEIVE Graph That Enlighten

Features of a Dotplot Displays the shape of the distribution of data It is usually possible to recreate the original list of data values

Example: Construct a dotplot for the following data set. 62 70 72 78 70 66 68 70 82 74 60 62 66

DEFINITION Dotplots: A dotplot consists of a graph of quantitative data in which each data value is plotted as a point or a dot above a horizontal scale of values. Dots representing equal values are stacked.

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Features of a Stemplot:

Shows the shape of the distribution of the data Retains the original data values The sample data are sorted (arranged) in order

Example: Listed below are pulse rates (beats per minutes) of females. Construct a stemplot.

80 94 58 66 56 82 78 86 88 56 36 66 84 76 78 64 66 78 60 64

DEFINITION: Stemplots: A stemplot (or stem and leaf plot) represents quantitative data by separating each value into two parts: the stem (such as the leftmost digit) and the leaf ((such as the rightmost digit). Better stemplots are usually obtained my rounding the original data values. Also stemplots can be expanded to include more rows and can be condensed to include fewer rows.

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Feature of a Time-Series Graph:

Reveals information about trends over time

Feature of a Bar Graph Shows the relative distribution of categorical data so that it is easy to compare the different categories

DEFINITION: A Bar Graph uses bars of equal width to show frequencies of categories of categorical (or qualitative) data. The bars may or may not be separated by small gaps.

DEFINITION Time-series graph: A time-series graph is a graph of time-series data, which are quantitative data that have been collected at different points in time, such as monthly or yearly.

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Features of a Pareto Chart

Shows the relative distribution of categorical data so that it is easier to compare the different categories

Draws attention to the more important categories Example: The Bar graph above is also a Pareto chart. Example: A sample of 521 adults was asked, “How often do you dine out?” the results of the survey are given in the table. Construct a Pareto chart. Response Frequency Several times a week 103 Once or twice a week 204 A few times a month 130 Very rarely 79 Never 5

0

10000000

20000000

30000000

40000000

50000000

Dogs Cats Birds Horses

Households who own

Households who own

DEFINITION: A Pareto chart is a bar graph for categorical data with the added stipulation that the bars are arranged in descending order according to frequencies, so the bars decrease in height from left to right.

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Feature of a Pie Chart: Shows the distribution of categorical data in a commonly used format.

Note: Degree of the sector = 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ∙ 360°

Example: A sample of 521 adults was asked, “How often do you dine out?” the results of the survey are given in the table. Construct a pie chart. Response Frequency Several times a week 103 Once or twice a week 204 A few times a month 130 Very rarely 79 Never 5

DEFINITION A pie chart is a very common graph that depicts categorical data as slices of a circle in which the size of each slice is proportional to the frequency count for the category. Although pie charts are very common, they are not as effective as Pareto charts.

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Example: The following data represent the top speed (in km/hr) of all the players (except goaltenders) in the 2014 World Cup Soccer Tournament. Construct a histogram and a frequency polygon. Speed (km/hr) Number of Players

10 – 13 4

14 -17 7

18 -21 17

22 – 25 91

26 -29 282

30 – 33 206

DEFINITION A frequency polygon uses line segments connected to points located directly above the class midpoint values. This is very similar to a histogram but uses lines instead of bars.

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GRAPHS THAT DECEIVE NONZERO AXIS: Always examine a graph carefully to see whether a vertical axis begin at some point other than zero so that differences can be exaggerated.

PICTOGRAPHS Drawings of objects called pictographs, are often misleading. Data that are one-dimensional in nature, such as budget amounts are often depicted using two-dimensional objects, such as dollar bills or three-dimensional objects such as stacks of coins, homes, or barrels. By using a pictograph an artist can create false impressions that grossly distort differences by using these simple principles of geometry

1. When you double each side of a square, its area doesn’t merely double, it increases by a factor of four

2. When you double each side of a cube it increases by a factor of eight

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